Import Question JSON

Current Question (ID: 20192)

Question:

$\text{Two conducting solid spheres } A \text{ and } B \text{ are placed at a very large distance with charge densities and radii as shown. When the key } K \text{ is closed, the ratio of final charge densities will be:}$ $\sigma, R$ $A$ $K$ $\sigma, 2R$ $B$

Options:

1. $4:1$
2. $1:2$
3. $2:1$
4. $1:4$

Solution:

$\text{Final potential is same:}$ $\Rightarrow \frac{1}{4\pi\varepsilon_0} \times \frac{Q_1}{R} = \frac{1}{4\pi\varepsilon_0} \times \frac{Q_2}{2R} \ldots (1)$ $\text{Also, } Q_1 + Q_2 = \sigma \cdot 4\pi R^2 + \sigma \cdot 4\pi (2R)^2 \ldots (2)$ $\text{From (1) and (2) } \frac{\sigma_1}{\sigma_2} = 2$

Import JSON File

Upload a JSON file containing LaTeX/MathJax formatted question, options, and solution.

Expected JSON Format:

{
  "question": "The mass of carbon present in 0.5 mole of $\\mathrm{K}_4[\\mathrm{Fe(CN)}_6]$ is:",
  "options": [
    {
      "id": 1,
      "text": "1.8 g"
    },
    {
      "id": 2,
      "text": "18 g"
    },
    {
      "id": 3,
      "text": "3.6 g"
    },
    {
      "id": 4,
      "text": "36 g"
    }
  ],
  "solution": "\\begin{align}\n&\\text{Hint: Mole concept}\\\\\n&1 \\text{ mole of } \\mathrm{K}_4[\\mathrm{Fe(CN)}_6] = 6 \\text{ moles of carbon atom}\\\\\n&0.5 \\text{ mole of } \\mathrm{K}_4[\\mathrm{Fe(CN)}_6] = 6 \\times 0.5 \\text{ mol} = 3 \\text{ mol}\\\\\n&1 \\text{ mol of carbon} = 12 \\text{ g}\\\\\n&3 \\text{ mol carbon} = 12 \\times 3 = 36 \\text{ g}\\\\\n&\\text{Hence, 36 g mass of carbon present in 0.5 mole of } \\mathrm{K}_4[\\mathrm{Fe(CN)}_6].\n\\end{align}",
  "correct_answer": 4
}